5 ms·

As an american who went through US-based curriculum in the 90s, this sounds FUCKING WONDERFUL. Basically - it seems like the approach above treats math as a co

As an american who went through US-based curriculum in the 90s, this sounds FUCKING WONDERFUL. Basically - it seems like the approach above treats math as a conceptual playground, where you should develop intuition and understanding. Instead we seem to be going down the rote memorization route for most of our classes, where the goal was to apply an equation to some numbers and get the right answer, with little to no thought, and an emphasis on easy grading. ---- Our physics education seems quite similar, though - and I loved that.

BoxOfRain 5y ago
My British state education really did feel like "memorise just enough to jump through these arbitrary hoops which keep the government off our backs" sometimes. It's very exam-driven rather than learning for its own sake and apparently it's got even worse since schools started transitioning to academies and Gove's reforms took effect.
- cabalamat 5y ago
  One fix for this is to have exam questions such that you cannot pass them unless you have true understanding rather than rote memorisation.
  - nicoburns 5y ago
    That's one part of the equation, but it only works if you have teachers and a curriculum that are capable of imparting that understanding.
  - fiftyacorn 5y ago
    Normally the curriculum was split between knowledge and understanding, and problem solving. You could memorize the first part and not the second part. The problem solving sorted out who got the grades
selimnairb 5y ago
I have always liked math, but have never been great or very good at it. I graduated from a US public school gifted program, and a top 30 US university. The biggest problem I always had with math education is they didn’t teach the “why” nearly enough. I was lousy at memorizing formulas/methods (esp. in calculus), so I often found myself dead in the water during exams.
- zsmi 5y ago
  I used to suffer from the lack of "why" too until one day it dawned on me that there really isn't a why, or maybe, the why is always the same: for engineers doing classical physics solving problems by hand, it's convenient to define it that way. No more, no less. When I was a math tutor in school, everyone would complain about lack of why. This was my approach to address the issue. I would describe a problem relevant to the class, say something like find the angle between two vectors, and ask them to think of a general way to do it. Usually this require some help from me but the solution was always "theirs". Then we would play with their solution: find corner cases, figure out which operations broke, develop a couple of theorems with it. Then I would show them the dot product, and a couple of its tricks (a.k.a. theorems), and they would get a good appreciation for why the dot product works the ways it does. And that's the why and the reason it stuck. It's useful way to solve a common problem. There is no magic or deep philosophical truth. The problem is this teaching style works with a dialog to a few number of students. I am not sure how well it would work in a lecture setting. It was also not so easy on me as I would be the person who had to spot the problems in their definition, basically on the spot, and lead them to it on their own without revealing the answer. With basic things like a dot product it's pretty easy to know where to look (i.e. is their definition commutative, pretty much never) and finding issues and nudging them too it wasn't too hard. But it's likely hard to scale things like this on many metrics.
  - iammisc 5y ago
    The problem with asking teachers to think on the spot is that teachers in America are especially dumb: https://www.forbes.com/sites/nataliewexler/2019/03/13/why-so-many-aspiring-teachers-cant-pass-a-licensing-test--and-why-it-matters/?sh=64db8b0f321a https://www.forbes.com/sites/nataliewexler/2019/03/13/why-so... My mother was a public school teacher. She passed her test on the first try, which was extremely rare at her school. She was taught in India, and became an American teacher as an older woman. She was an outlier. She graduated from a major public teaching program in our state of California (CSU Fullerton). Most teachers fail their tests on the first try. This is not advanced calculus... this is elementary mathematics and reading. The issue is that accolades in the education department do not translate to results. The state creates a monopoly on teaching via its certification process, with means education departments are guaranteed funding regardless of their results, given that once you have the credential, you're considered 'equal' to other teachers. Despite my mother doing very well on her tests, she was fired and not granted tenure because she didn't follow her principal's teaching methodology. Even though her students were passing their own exams at higher rates and doing better (And of course my mother taught two boys who went on to make careers in science and mathematics), she was fired for not following the failing methodology. This is what is wrong with American schooling. It's a race to the bottom and the teachers have no idea what's actual achievement because they've never achieved basic elementary schooling, much less seen it in others. Here are example questions: https://www.mometrix.com/academy/praxis-math-practice-test/ https://www.mometrix.com/academy/praxis-math-practice-test/ These are not difficult, at all. EDIT: in some ways america is doomed by its own success, in that, for those who can actually do math, reading, and writing, there are significantly more lucrative fields than teaching. Unfortunately, since teachers can't teach those skills, it's really a new aristocracy formed by parents who do know those skills passing them on to children.
jnsie 5y ago
Same in Ireland :-(
ponkon 5y ago
Also American, but was routed through, what was at the time, an experimental program called Integrated Math. Class was structured around word problems and the students were guided towards figuring out the formulas rather than rote memorization. There was a ton of group work, which worked out really well for me, but if you didn't want to learn it was pretty easy to coast and let the group leader do most of the work / learning.
beamatronic 5y ago
I could do calculus, in high school and college, but I wasn't very happy about it. Until I took a physics class in college which happened to be intended for the physics majors. Did the professor ever just present an equation and ask us to learn it? No! Every Single Physics Equation was explained from first principles, using calculus - a lot of integrals. Finally we were seeing a practical application, where calculus was just a tool to get you where you needed to be.
- DavidPeiffer 5y ago
  I was a bit disappointed to see the differences between "algebra based physics" in high school and "Calc based physics" in college. It wasn't a whole lot more than "now rather than giving you formulas, do an integral to go from acceleration to speed, or speed to position". It did feel good to see a practical use for the calculus I had learned, much more so than determining how much the surface area changed after adding a layer of paint 0.01" thick to a tank.
- sudobash1 5y ago
  It was really helpful to me in highschool that the calculus teacher was also the physics teacher, and many students were enrolled in both classes simultaneously. You ended up learning both at the same time.
  - QuercusMax 5y ago
    Teaching calculus through physics (and vice versa) actually makes a lot of sense. Similarly, basic Linear Algebra and 3D graphics have great synergy. I took LinAlg and Computer Graphics the same semester in undergrad, and the first half of LinAlg led perfectly into the second half of CG. (The first half of CG was all 2D stuff, which didn't need any special math.)

BoxOfRain 5y ago

My British state education really did feel like "memorise just enough to jump through these arbitrary hoops which keep the government off our backs" sometimes. It's very exam-driven rather than learning for its own sake and apparently it's got even worse since schools started transitioning to academies and Gove's reforms took effect.

cabalamat 5y ago
One fix for this is to have exam questions such that you cannot pass them unless you have true understanding rather than rote memorisation.
- nicoburns 5y ago
  That's one part of the equation, but it only works if you have teachers and a curriculum that are capable of imparting that understanding.
- fiftyacorn 5y ago
  Normally the curriculum was split between knowledge and understanding, and problem solving. You could memorize the first part and not the second part. The problem solving sorted out who got the grades

selimnairb 5y ago

I have always liked math, but have never been great or very good at it. I graduated from a US public school gifted program, and a top 30 US university. The biggest problem I always had with math education is they didn’t teach the “why” nearly enough. I was lousy at memorizing formulas/methods (esp. in calculus), so I often found myself dead in the water during exams.

zsmi 5y ago
I used to suffer from the lack of "why" too until one day it dawned on me that there really isn't a why, or maybe, the why is always the same: for engineers doing classical physics solving problems by hand, it's convenient to define it that way. No more, no less. When I was a math tutor in school, everyone would complain about lack of why. This was my approach to address the issue. I would describe a problem relevant to the class, say something like find the angle between two vectors, and ask them to think of a general way to do it. Usually this require some help from me but the solution was always "theirs". Then we would play with their solution: find corner cases, figure out which operations broke, develop a couple of theorems with it. Then I would show them the dot product, and a couple of its tricks (a.k.a. theorems), and they would get a good appreciation for why the dot product works the ways it does. And that's the why and the reason it stuck. It's useful way to solve a common problem. There is no magic or deep philosophical truth. The problem is this teaching style works with a dialog to a few number of students. I am not sure how well it would work in a lecture setting. It was also not so easy on me as I would be the person who had to spot the problems in their definition, basically on the spot, and lead them to it on their own without revealing the answer. With basic things like a dot product it's pretty easy to know where to look (i.e. is their definition commutative, pretty much never) and finding issues and nudging them too it wasn't too hard. But it's likely hard to scale things like this on many metrics.
- iammisc 5y ago
  The problem with asking teachers to think on the spot is that teachers in America are especially dumb: https://www.forbes.com/sites/nataliewexler/2019/03/13/why-so-many-aspiring-teachers-cant-pass-a-licensing-test--and-why-it-matters/?sh=64db8b0f321a https://www.forbes.com/sites/nataliewexler/2019/03/13/why-so... My mother was a public school teacher. She passed her test on the first try, which was extremely rare at her school. She was taught in India, and became an American teacher as an older woman. She was an outlier. She graduated from a major public teaching program in our state of California (CSU Fullerton). Most teachers fail their tests on the first try. This is not advanced calculus... this is elementary mathematics and reading. The issue is that accolades in the education department do not translate to results. The state creates a monopoly on teaching via its certification process, with means education departments are guaranteed funding regardless of their results, given that once you have the credential, you're considered 'equal' to other teachers. Despite my mother doing very well on her tests, she was fired and not granted tenure because she didn't follow her principal's teaching methodology. Even though her students were passing their own exams at higher rates and doing better (And of course my mother taught two boys who went on to make careers in science and mathematics), she was fired for not following the failing methodology. This is what is wrong with American schooling. It's a race to the bottom and the teachers have no idea what's actual achievement because they've never achieved basic elementary schooling, much less seen it in others. Here are example questions: https://www.mometrix.com/academy/praxis-math-practice-test/ https://www.mometrix.com/academy/praxis-math-practice-test/ These are not difficult, at all. EDIT: in some ways america is doomed by its own success, in that, for those who can actually do math, reading, and writing, there are significantly more lucrative fields than teaching. Unfortunately, since teachers can't teach those skills, it's really a new aristocracy formed by parents who do know those skills passing them on to children.

jnsie 5y ago

Same in Ireland :-(

ponkon 5y ago

Also American, but was routed through, what was at the time, an experimental program called Integrated Math. Class was structured around word problems and the students were guided towards figuring out the formulas rather than rote memorization. There was a ton of group work, which worked out really well for me, but if you didn't want to learn it was pretty easy to coast and let the group leader do most of the work / learning.

beamatronic 5y ago

I could do calculus, in high school and college, but I wasn't very happy about it. Until I took a physics class in college which happened to be intended for the physics majors. Did the professor ever just present an equation and ask us to learn it? No! Every Single Physics Equation was explained from first principles, using calculus - a lot of integrals. Finally we were seeing a practical application, where calculus was just a tool to get you where you needed to be.

DavidPeiffer 5y ago
I was a bit disappointed to see the differences between "algebra based physics" in high school and "Calc based physics" in college. It wasn't a whole lot more than "now rather than giving you formulas, do an integral to go from acceleration to speed, or speed to position". It did feel good to see a practical use for the calculus I had learned, much more so than determining how much the surface area changed after adding a layer of paint 0.01" thick to a tank.
sudobash1 5y ago
It was really helpful to me in highschool that the calculus teacher was also the physics teacher, and many students were enrolled in both classes simultaneously. You ended up learning both at the same time.
- QuercusMax 5y ago
  Teaching calculus through physics (and vice versa) actually makes a lot of sense. Similarly, basic Linear Algebra and 3D graphics have great synergy. I took LinAlg and Computer Graphics the same semester in undergrad, and the first half of LinAlg led perfectly into the second half of CG. (The first half of CG was all 2D stuff, which didn't need any special math.)